E. Nualart

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math.PR2026

On the local well-posedness of randomly forced reaction-diffusion equations with $L^{2}$ initial data and a superlinear reaction term

Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart

We consider a parabolic stochastic partial differential equation (SPDE) on $[0, 1]$ that is forced with multiplicative space-time white noise with a bounded and Lipschitz diffusio…

math.PR2025

On the well-posedness of SPDEs with locally Lipschitz coefficients

Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart

We consider the stochastic partial differential equation, $\partial_{t} u = \frac{1}{2} \partial_{x}^{2} u + b (u) + I ¨ (u) W ˙,$ where $u = u (t, x)$ is defined for $(t\,,x)\in(0\,,\infty)…

math.PR2025

Multivariate Poisson approximation of joint subgraph counts in random graphs via size-biased couplings

Eulalia Nualart, Rui-Ray Zhang

Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study…

On the local well-posedness of randomly forced reaction-diffusion equations with L2 initial data and a superlinear reaction term

On the well-posedness of SPDEs with locally Lipschitz coefficients

Multivariate Poisson approximation of joint subgraph counts in random graphs via size-biased couplings

On the local well-posedness of randomly forced reaction-diffusion equations with $L^{2}$ initial data and a superlinear reaction term